scholarly journals Numerical Solution of Axisymmetric Inverse Heat Conduction Problem by the Trefftz Method

Energies ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 705
Author(s):  
Sylwia Hożejowska ◽  
Magdalena Piasecka
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Boiling Heat Transfer ◽  
Flow Boiling ◽  
Heated Surface ◽  
Essential Element ◽  
Trefftz Method ◽  
Flowing Fluid ◽  
The Heat Transfer Coefficient

In this paper, the issue of flow boiling heat transfer in an annular minigap was discussed. The main aim of the paper was determining the boiling heat transfer coefficient at the HFE-649 fluid–heater contact during flow along an annular minigap. The essential element of the experimental stand was a test section vertically oriented with the minigap 2 mm wide. Thermocouples were used to measure the temperature of the heater and fluid at the inlet and the outlet to the minigap. The mathematical model assumed that the fluid flow was laminar and the steady–state heat transfer process was axisymmetric. The temperatures of the heated surface and of the flowing fluid were assumed to fulfill energy equations with adequate boundary conditions. The problem was solved by the Trefftz method. The local heat transfer coefficients at the fluid–test surface interface were calculated due to the third kind boundary condition at the saturated boiling. Graphs were used to illustrate: the measurement of the heater surface temperature, 2D temperature distributions in the pipe and fluid, and the heat transfer coefficient as a function of the distance from the minigap inlet. The measurement uncertainties and accuracy of the heat transfer coefficient determination were estimated.

scholarly journals Cooling liquid flow boiling heat transfer in an annular minigap with an enhanced wall

2019 ◽  
Vol 213 ◽  
pp. 02066 ◽  
Author(s):  
Magdalena Piasecka ◽  
Tomasz Musiał ◽  
Artur Piasecki
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Boiling Heat Transfer ◽  
Flow Boiling ◽  
Heated Surface ◽  
Metal Pipe ◽  
Flow Boiling Heat Transfer ◽  
Enhanced Surface ◽  
The Heat Transfer Coefficient

The paper focused on flow boiling heat transfer in an annular minigap. This gap of 1 mm width was created between the metal pipe with an enhanced surface contacting fluid and the external glass pipe positioned along the same axis. The heated element for the HFE-649 flowing in the minigap was a cartridge heater. Thermocouples were used to measure the temperature of the metal pipe in the contact surface with a fluid. The local values of the heat transfer coefficient for stationary state conditions were calculated using an one-dimensional method in which the multilayer cylindrical wall was assumed to be planar. The results were presented as a function of the heat transfer coefficient along the minigap length and as boiling curves, prepared for selected values of mass flow rate and five types of the enhanced heated surface and a smooth one. Observations indicated that the highest local values of heat transfer coefficient were obtained with using the enhanced surface produced by electromachining process (spark erosion) at the saturated boiling region. The boiling curves generated for two distances from the minigap inlet have similar plots without a drop in the temperature of the heated surface characteristic for nucleation hysteresis.

scholarly journals The heat transfer coefficient determination with the use of the Beck-Trefftz method in flow boiling in a minichannel

2018 ◽  
Vol 180 ◽  
pp. 02099 ◽  
Author(s):  
Kinga Strąk ◽  
Beata Maciejewska ◽  
Magdalena Piasecka
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Boiling Heat Transfer ◽  
Transfer Problem ◽  
Heat Conduction Problem ◽  
Flow Boiling ◽  
Inverse Heat Conduction Problem ◽  
Heated Wall ◽  
Trefftz Method

In this paper, the solution of the two-dimensional inverse heat transfer problem with the use of the Beck method coupled with the Trefftz method is proposed. This method was applied for solving an inverse heat conduction problem. The aim of the calculation was to determine the boiling heat transfer coefficient on the basis of temperature measurements taken by infrared thermography. The experimental data of flow boiling heat transfer in a single vertical minichannel of 1.7 mm depth, heated asymmetrically, were used in calculations. The heating element for two refrigerants (FC-72 and HFE-7100, 3M) flowing in the minichannel was the plate enhanced on the side contacting with the fluid. The analysis of the results was performed on the basis of experimental series obtained for the same heat flux and two different mass flow velocities. The results were presented as infrared thermographs, heated wall temperature and heat transfer coefficient as a function of the distance from the minichannel inlet. The results was discussed for the subcooled and saturated boiling regions separately.

Study on Flow Boiling Heat Transfer of Carbon Dioxide With PAG-Type Lubricating Oil in Pre-Dryout Region Inside Horizontal Tube

2010 ◽  
Author(s):  
Chaobin Dang ◽  
Minxia Li ◽  
Eiji Hihara
Keyword(s):  
Heat Transfer ◽  
Carbon Dioxide ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Mass Flux ◽  
Boiling Heat Transfer ◽  
Flow Boiling ◽  
Nucleate Boiling ◽  
Flow Boiling Heat Transfer ◽  
The Heat Transfer Coefficient

In this study, the boiling heat transfer coefficients of carbon dioxide with a PAG-type lubricating oil entrained from 0 to 5 wt% in a horizontally placed smooth tube with an inner diameter of 2 mm were experimentally investigated under the following operating conditions: mass fluxes from 170 to 320 kg/m2s, heat fluxes from 4.5 to 36 kW/m2, and a saturation temperature of 15 °C. The results show that for a low oil concentration of approximately 0.5% to 1%, no further deterioration of the heat transfer coefficient was observed at higher oil concentrations in spite of a significant decrement of the heat transfer coefficient compared to that under an oil-free condition. The heat flux still had a positive influence on the heat transfer coefficient in low quality regions. However, no obvious influence was observed in high quality regions, which implies that nucleate boiling dominates in the low quality region whereas it is suppressed in the high quality regions. Unlike the mass flux under an oil-free condition, mass flux has a significant influence on the heat transfer coefficient, with a maximum increase of 50% in the heat transfer. On the basis of our experimental measurements of the flow boiling heat transfer of carbon dioxide under wide experimental conditions, a flow boiling heat transfer model for horizontal tubes has been proposed for a mixture of CO2 and polyalkylene glycol (PAG oil) in the pre-dryout region, with consideration of the thermodynamic properties of the mixture. The surface tension and viscosity of the mixture were particularly taken into account. New factors were introduced into the correlation to reflect the suppressive effects of the mass flux and the oil on both the nucleate boiling. It is shown that the calculated results can depict the influence of the mass flux and the heat flux on both nucleate boiling and convection boiling.

Flow Boiling Heat Transfer Characteristics of a Minichannel Up to Dryout Condition

2009 ◽  
Author(s):  
Rashid Ali ◽  
Bjo¨rn Palm ◽  
Mohammad H. Maqbool
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Mass Flux ◽  
Boiling Heat Transfer ◽  
Flow Boiling ◽  
Working Fluid ◽  
Flow Boiling Heat Transfer ◽  
The Heat Transfer Coefficient

In this paper the experimental flow boiling heat transfer results of a minichannel are presented. A series of experiments was conducted to measure the heat transfer coefficients in a minichannel made of stainless steel (AISI 316) having an internal diameter of 1.7mm and a uniformly heated length of 220mm. R134a was used as working fluid and experiments were performed at two different system pressures corresponding to saturation temperatures of 27 °C and 32 °C. Mass flux was varied from 50 kg/m2 s to 600 kg/m2 s and heat flux ranged from 2kW/m2 to 156kW/m2. The test section was heated directly using a DC power supply. The direct heating of the channel ensured uniform heating and heating was continued until dry out was reached. The experimental results show that the heat transfer coefficient increases with imposed wall heat flux while mass flux and vapour quality have no considerable effect. Increasing the system pressure slightly enhances the heat transfer coefficient. The heat transfer coefficient is reduced as dryout is reached. It is observed that dryout phenomenon is accompanied with fluctuations and a larger standard deviation in outer wall temperatures.

Flow Boiling Heat Transfer Characteristics of a Minichannel up to Dryout Condition

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Rashid Ali ◽  
Björn Palm ◽  
Mohammad H. Maqbool
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Mass Flux ◽  
Boiling Heat Transfer ◽  
Flow Boiling ◽  
Working Fluid ◽  
Flow Boiling Heat Transfer ◽  
The Heat Transfer Coefficient

In this paper, the experimental flow boiling heat transfer results of a minichannel are presented. A series of experiments was conducted to measure the heat transfer coefficients in a minichannel made of stainless steel (AISI 316) having an internal diameter of 1.70 mm and a uniformly heated length of 220 mm. R134a was used as a working fluid, and experiments were performed at two different system pressures corresponding to saturation temperatures of 27°C and 32°C. Mass flux was varied from 50 kg/m2 s to 600 kg/m2 s, and heat flux ranged from 2 kW/m2 to 156 kW/m2. The test section was heated directly using a dc power supply. The direct heating of the channel ensured uniform heating, which was continued until dryout was reached. The experimental results show that the heat transfer coefficient increases with imposed wall heat flux, while mass flux and vapor quality have no considerable effect. Increasing the system pressure slightly enhances the heat transfer coefficient. The heat transfer coefficient is reduced as dryout is reached. It is observed that the dryout phenomenon is accompanied with fluctuations and a larger standard deviation in outer wall temperatures.

scholarly journals Comparison of the 1D and 2D calculation models used for determination of the heat transfer coefficient during flow boiling heat transfer in a minichannel

2019 ◽  
Vol 128 ◽  
pp. 01017
Author(s):  
Kinga Strak ◽  
Magdalena Piasecka ◽  
Beata Maciejewska
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Boiling Heat Transfer ◽  
Flow Boiling ◽  
Outer Side ◽  
Plate Temperature ◽  
Flow Boiling Heat Transfer ◽  
The Heat Transfer Coefficient ◽  
Calculation Models

The paper discusses the results of the flow boiling heat transfer in a vertical minichannel with rectangular cross-section. The heating element for FC-72 flowing in the minichannel is a thin plate. Infrared thermography is used to determine changes in the temperature on its outer side. The aim of thecalculation is to determine the heat transfer coefficient using 1D and 2D calculation models. Local values of heat transfer coefficient on the surface between the heated plate and boiling fluid are calculated from the Newton`s and Fourier`s laws. In 2D model the plate temperature distribution is obtained by solving the inverse heat conduction problem. The governing equation is solved by means of two methods: the non-continuous Trefftz method and the Beck method. The results are presented as plate temperature and heat transfer coefficient calculated using 1D and 2D models as a function of the distance fromthe minichannel inlet. The analysis of the results revealed that the values and distributions of the heat transfer coefficient calculated by means of both models were similar. This suggests that all mentioned methods are interchangeable.

Analytical Modeling of Annular Flow Boiling Heat Transfer in Mini- and Microchannel Heat Sinks

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
A. Megahed ◽  
I. Hassan
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Analytical Model ◽  
Boiling Heat Transfer ◽  
Annular Flow ◽  
Flow Boiling ◽  
Heat Sinks ◽  
Flow Boiling Heat Transfer ◽  
The Heat Transfer Coefficient

An analytical model is proposed to predict the flow boiling heat transfer coefficient in the annular flow regime in mini- and microchannel heat sinks based on the separated model. The modeling procedure includes a formulation for determining the heat transfer coefficient based on the wall shear stress and the local thermophysical characteristics of the fluid based on the Reynolds’ analogy. The frictional and acceleration pressure gradients within the channel are incorporated into the present model to provide a better representation of the flow conditions. The model is validated against collected data sets from the literature produced by different authors under different experimental conditions, different fluids, and with mini- and microchannels of hydraulic diameters falling within the range of 92–1440 μm. The accuracy between the experimental and predicted results is achieved with a mean absolute error of 10%. The present analytical model can correctly predict the different trends of the heat transfer coefficient reported in the literature as a function of the exit quality. The predicted two-phase heat transfer coefficient is found to be very sensitive to changes in mass flux and saturation temperature. However, it is found to be mildly sensitive to the change in heat flux.

scholarly journals Time-Dependent Heat Transfer Calculations with Trefftz and Picard Methods for Flow Boiling in a Mini-Channel Heat Sink

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1832
Author(s):  
Magdalena Piasecka ◽  
Sylwia Hożejowska ◽  
Beata Maciejewska ◽  
Anna Pawińska
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Heat Sink ◽  
Flow Boiling ◽  
Time Dependent ◽  
Heated Wall ◽  
Trefftz Method ◽  
Mini Channels ◽  
The Heat Transfer Coefficient

The intensification of heat transfer using two-phase boiling flow in mini-channels is widely used to dissipate the high heat fluxes in miniaturized electronic devices. However, the process itself is not fully recognized and still requires experimental studies and developing computation methods appropriate for them. The main aim of this work was the mathematical modeling of time-dependent heat transfer process in FC-72 flow boiling in a mini-channel heat sink with five parallel mini-channels of 1 mm depth. Channels have an asymmetrically heated wall while its outer temperature was measured by infrared thermography. The opposite wall of the mini-channels was transparent, helping to record flow patterns due to a high-speed digital camera. The objective of the numerical calculations was to determine the heat transfer coefficient on the wall-fluid contact surface from the Robin boundary condition. The problem was solved using methods based on the Trefftz-type functions. Three mathematical methods were applied in calculations: the FEM with Trefftz type basis functions, the Classical Trefftz Method, and the Hybrid Picard-Trefftz Method. The results were compared with the values of the heat transfer coefficient obtained from theoretical correlations from the literature.

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